chap4_8.m

利用MATLAB解决<偏微分方程数值算法>中的一些问题,如插值求解

function[Y1,Y2,E1]=chap4_8(h,tao,A)   %习题4.8
 a=1;s=a*tao/h;
for k=1:1/tao+1
  for i=1:1/h+1
      U(k,i)=0;
  end
end
for i=1:1/h+1
    X(1,i)=(i-1)*h;U(1,i)=0;
end
for i=1:1/h+1
    X(1,i)=(i-1)*h;U(2,i)=tao*X(1,i)+U(1,i);
end
for k=1:1/tao+1
    T(1,k)=(k-1)*tao;U(k,1)=0;U(k,1/h+1)=sin(T(1,k));
end
for i=1:1/h-1
    for j=1:1/h-1
        Z(i,j)=0;
    end
end
for i=1:1/h-1
    Z(i,i)=1+s^2;
end
for i=2:1/h-1
    Z(i,i-1)=-1/2*s^2;
    Z(i-1,i)=-1/2*s^2;
end
    for k=3:1/tao+1
    for j=2:1/h
        B(j-1,1)=tao^2*(T(1,k-1)^2-X(1,i)^2)*sin(X(1,i)*T(1,k-1))+2*U(k-1,j);
end
    B(1,1)=B(1,1)+1/2*s^2*(U(k,1)+U(k-2,1));
    B(1/h-1,1)=B(1/h-1,1)+1/2*s^2*(U(k,1/h+1)+U(k-2,1/h+1));
    U([k],2:1/h)=(inv(Z)*(B+(-1)*Z*(U([k-1],2:1/h))'))';
end
for j=1:length(A)
Y1(1,j)=U(ceil(A(1,j)/tao+1),ceil(0.5/h+1));%ceil()为加入正小数至最近整数．
Y2(1,j)=sin(0.5*A(1,j));E1(1,j)=abs(Y1(1,j)-Y2(1,j));
end
end